For a few years, we have been seeing a growing number of bicycles assisted by electric motor coming onto the market. These bicycles are actually designed for the cyclist to work with his assistance and the electric motor cannot move the bicycle on its own, as in prior embodiments. The input from the cyclist makes it possible to extend the action radius by a little, whereas the assistance provides the user with the sensation of being very fit.
These vehicles are far from being all equivalent in their effectiveness; they differ by their motor, the kinematics through which it acts, the management of the assistance, the batteries and the bicycle on which the assistance is mounted.                The motors of this type of vehicle nearly all have a rated power of approximately 200 watts, or the equivalent of what the occasional cyclist can give at his maximum. On the other hand, they differ by their speed of rotation, their torque curve, their efficiency curve, their cooling, their noise, their weight and their price.        
However, with regard to our concerns, we will say that they are all fairly close and share essential qualities for this assistance work. They start on their own, offer a significant torque on stopping and at low speeds, often revolve slowly (some are even directly geared), are fairly silent, vibrate little, and have a fairly good efficiency provided that they are not made to rotate too slowly.
All these qualities, we should say immediately, are cruelly lacking on heat engines.                The kinematics of the assistance motor is a crucial point of difference between these bicycles.        
On many of these assistances, the motor has a single transmission ratio, which means that it can deliver its rated power only at a single speed (often 25 km/h). The consequence of this arrangement is that the assistance power drops with the speed, which is a nuisance in head winds and dramatic on climbs. This problem is reinforced by a drop in the efficiency (reduction of the autonomy) and a motor which will rapidly overheat, so much so that these bicycles are unsuited to reliefs, even if the kinematics of the cyclist offers a number of ratios.
On another, much more sophisticated, family of assistance, the motor will benefit from the changes of ratio of the cyclist, so that the cyclist and the motor can continue their good collaboration over the entire range of variation of the ratios of the bicycle.                The management of the assistance is also of prime importance. To satisfy certain laws, the motor must not operate if the cyclist is not pedaling, which is, moreover, the definition of an assistance. In fact, some bicycles do not obey this rule, but the low installed power limits to very few occasions when the bicycle is used without pedaling.        
It is very tempting to think that the assistances based on a measurement of the torque exerted on the pedal, with a proportional response from the motor, provide the most appropriate system. A finer approach shows that the torque that a cyclist exerts on his pedal is sinusoidal and, without any special arrangement, the response from the motor will also be sinusoidal over a pedal revolution. This detail deprives these bicycles of a huge advantage that the assistances could provide. In practice, if, on the flat, the inertia of the bicycle makes these torque variations insensitive, the same does not apply when climbing. There, the bicycle slows down at each dead point of the pedal to then accelerate. This is the reason why our average pedaling speed decreases when climbing and it is also the reason why, given equal power, pedaling on a slope is more trying than on the flat. This torque variation is also highly unfavorable to road holding, a particularly sensitive detail on all-terrain bicycles which have very limited capabilities in this respect.
Without going into the details, good management of the assistance gives a constant torque over a pedal revolution. This gives a constant torque bottom that makes it possible to easily pass the dead points of the pedal, and this considerable “rounds” the pedal stroke when climbing and when starting. The effect goes well beyond the added power, because it enables the cyclist to obtain, on a slope, a pedaling efficiency close to that of the flat.                The batteries are the enormous weakness of these vehicles, despite recent advances in the field and the basic research does not give room to hope for storage greater than 200 Wh/kg. In reality, we are very far from that because the energy storage depends on a large number of parameters: the temperature, the power drawn, the age of the battery, the number of recharges already made, the storage durations and the recharging modes. In reality, the best batteries offer an average of approximately 100 Wh/kg over two years of use.        
If we use the analogy with a liquid fuel, even by taking into account the efficiency difference between an electric motor and a heat engine, a kilo of battery is at best equivalent to a 50 cm3 tank that would have to be drip-fed for at least four hours, that would shrink on each filling, that would leak when it is not being used, that would generally burst after three years, in which the calorific value of the fuel would drop with its level, and that would be produced in a non-recyclable, very precious metal.
This analogy, which seems like a caricature, defines the challenge that these bicycles have to overcome.
It should be noted that a kilo of lithium-ion battery costs approximately 200 euros (2007) and it will store, at best, in its life, 500×100 wh, or 50 kwh, or approximately 5 euros of energy. The price of the storage is therefore 40 times the price of the stored energy.
This detail becomes apparent in all its cruelty when the user has to change his battery (generally after two to three seasons) and surveys show that the life of said bicycle often stops there.
All this means that these bicycles carry with them a derisory quantity of energy, approximately one hour at rated power. In some countries, laws dictate that these bicycles have maximum speeds (25 to 32 km/h), and indeed, most of these assistances are cut off at 18 km/h to save on energy and there is then no assistance on starting. This makes it possible, depending on the manufacturer's measurement protocol, to announce autonomies that sometimes exceed 80 kms. In truth, most of this distance will be covered with zero or very low assistance. When climbing, for those bicycles that are capable thereof, the autonomy generally remains less than 10 kms.
This is truly regrettable, because some of these vehicles are truly successful, their user-friendliness is such that it would be possible to be unaware that you were on a motorized vehicle and only think that you were in dazzling form. In towns they make it possible to cover ten or so kilometers in hot conditions without perspiring, and there is less hesitation to brake or stop when starting is easy, which is all for the benefit of safety. We would say, for the best of them, that they are formidable . . . for one hour. This represents a very restricted use, prohibits any trips, and greatly limits their circulation.
The idea of a bicycle assisted with liquid fuel sourced from fossil or vegetable matter resolves all the energy storage problems, but the current heat engines do not have any of the characteristics specific to electric motors.
They do not start on their own, they have a minimum slowing down speed, have little torque at very low speeds, this torque is highly variable over the cycle of the engine, they have a restricted range of use, a fairly low and variable efficiency depending on the load and speed, they overheat a lot, vibrate, make a lot of noise and can be highly polluting. However, they are the only ones whose technology is truly known, that are easy to implement and economical to produce. Also, later we will see some arrangements that make it possible to resolve or mitigate most of these drawbacks. These arrangements will make it possible to design a particularly agreeable vehicle, with surprising overall efficiency and astonishing discretion.
To want to bring together the user-friendliness of an electrically-assisted bicycle with a thermal assistance is not an easy objective. Each element must satisfy multiple constraints (notably function, weight, layout, ergonomics, efficiency, noise, vibration, compatibility with bicycle transmission, price), and these constraints are so important that some elements will hereinafter be described several times through each of these aspects.
Thousands of patents deal with bicycles equipped with a heat engine, but in most cases, the engine is intended to replace the pedaling. Collaboration is impossible, or possible only in very specific circumstances, for example when climbing at very low speed or when starting up.
Many conditions are necessary for permanent collaboration between the cyclist and his assistance to be possible and there will be many more thereof if we want this collaboration to be effective and harmonious and give good efficiency.
The first is that the respective transmission ratios of the cyclist and of the assistance are compatible over the entire speed range of the vehicle. This first condition limits the number of relevant patents to a few dozen. It would be quite difficult to give a summary here of the scope of these patents. We will therefore try to cite them within the limits of our knowledge as we progress through the general description that follows, when they seem relevant to us.
Without going into the fairly complex details that define the physiological efficiency of pedaling, we can state that the maximum efficiency of an occasional cyclist (who does not reach 0.2), lies at approximately 60 to 70 pedal revolutions per minute and his continuous maximum power at approximately 80 to 90 rpm.
Modern bicycle transmissions offer a large number of ratios and a big range of variation that can exceed 6, which means that they enable a cyclist to remain at his maximum efficiency for speeds ranging for example from 7 to 42 km/h. We will consider that they are fairly optimal, for most of the conditions encountered. The bicycle will therefore be equipped therewith.
The maximum efficiency of conventional heat engines fairly easily exceeds 0.25, so it is greater than human efficiency, but remains fairly low and this gives a great release of heat that must be treated correctly.
This efficiency is maximum only at full load and over a fairly narrow speed range and it bottoms out rapidly outside of these conditions. Note that the maximum efficiency speed is always close to the maximum torque speed.
The full load condition is fairly easy to resolve; it is sufficient for there to be almost never any excess power, and therefore for the installed power to be very low. This detail goes in the right direction, because with high power, the input from the cyclist would very quickly become negligible and superfluous.
The condition of holding to the maximum efficiency speed range is more difficult; it excludes all the single-transmission ratio kinematics, especially as, with low power, the speed of the vehicle will be extremely variable with the wind or the gradients encountered. (This condition considerably reduces the number of relevant patents.)
The first possible solution for resolving this problem is the variable speed drive, centrifugal or driven. This possible solution poses difficult technical problems in its application to the assisted bicycle.
Another fairly elegant solution is to use, for the engine, the change of speed of the cyclist, which is possible when the added power is low. In this case, the speed of rotation of the engine is proportionally linked to that of the pedaling.
It is then sufficient to choose the appropriate reduction ratio, so that the maximum engine efficiency speed broadly corresponds to the cyclist's maximum pedaling efficiency speed.
We immediately see that there would also be great interest in having the maximum power speeds also correspond. This is possible if the engine is defined to have the same ratios between maximum efficiency speeds and maximum power speeds as the cyclist, or approximately 65/85=0.76, which is quite possible.
Thus, the cyclist will manage his speeds as he has always done for himself, while placing the engine in the best arrangements to perform its work. Also, since man is by nature particularly economic in his energy management, when it is he who has to provide it, this leads to an assistance management system that is free and particularly optimized regarding the engine speed aspect, which is vitally important with a heat engine. This arrangement, accompanied by a low installed power which guarantees strong charge for the engine, leads to an installation that will mostly be used at its optimum efficiency.
As an indication, a comfortable bicycle (very straight position) equipped with large and underinflated tires may, despite everything, exceed 35 km/h, with 400 watts of power (with the same power, a racing bicycle reaches 50 km/h). These 400 watts can be distributed at 100 watts for the cyclist (very low) and 300 watts for the assistance. To supply these 300 watts to the bicycle, we will assume that the engine must supply 360 watts (a half horse power) to compensate for the transmission losses.
Good heat engines can reach an efficiency of 180 g of fuel per horse power per hour. Since we want a simple engine that will not always be exactly at its maximum efficiency, we will consider that it will use on average 220 g·hp·h, or 110 g of fuel per hour for our 360 watt engine.
It will take approximately 3 hours for our bicycle to cover 100 km, so its consumption will be 330 g of fuel, or a little under 0.5 liter if it is petrol, or the astonishing value of 12 g of CO2/km (in this area, the best cycle engines do not drop below 60 g of CO2/km).
Note that, despite assumptions that are always highly unfavorable, this value is not within the scope of an electric bicycle, unless the electricity is of nuclear or renewable source.
This idea is not truly novel since we can find traces of it at the start of the century in French patent No. 535 184, then later in the French patent No. 915 817, then notably in the U.S. Pat. No. 3,280,932, GB 637 014, U.S. Pat. No. 4,397,369, U.S. Pat. No. 5,076,386, U.S. Pat. No. 5,361,863, U.S. Pat. No. 5,941,332, EP 0 822 136 A2. And yet, very few productions have used this theoretically highly attractive technique.